You're fortunate to be in a great are for action shooting. There are plenty of IDPA matches in the area, and with its emphasis on standard gear, would be a good way to start.
There are IDPA top-notch outdoor matches at
The Range, and
Caswell Ranch.
PDHSC is an indoor range that hosts monthly IDPA matches, and the
Durham Wildlife Club holds IDPA matches every Tuesday evening. The matches at DWC and Caswell are particularly good for the new shooter, IMO.
You might want to consider USPSA as well. More "freestyle" than IDPA, and higher round count.
Sir Walter Raleigh Gun Club hosts an excellent USPSA match monthly.
Finally, there are also some "fun" matches that aren't beholding to strict IDPA or USPSA formats, and are more "run watcha brung". The Range has one monthly.
Another was recently started by a local shooter and is becoming popular quickly.